基于Mie散射理论的C@H2O复合粒子散射特性研究
【摘要】 大气中大量存在的复合粒子会对激光传输效率产生很大影响。为凝结核外层包裹以水的核壳结构微粒对光传输具有明显的散射效应MieC@H2O核壳结构微粒的散射特性进行了理论分析和数值计算，首先给出了不同入射波长核粒子半径以及水膜厚度、核粒子半径以及水膜厚度条件下偏振变化情况;条件下散射强度分布变化曲线;其次给出了不同入射波长、结果表明各参数对前向散射强度影响较大，入射波长越大散最后讨论了光学截面与粒子半径之间的关系核半径增大粒子的前向散射增强，水膜厚度增大粒子的前向散射增强，而后向散射无明显影射强度越弱，C响;入射波长较大时，粒子在多个角度出现线偏振光，入射波长增大水膜厚度增大，偏振度峰、值都会增多;随着入射波长的增大，散射截面最大峰值位置向着半径增大的方向移动，并伴随一定的振荡现象，散射和消光截面在碳核半径为碳核半径变大、左右达到最大值散射理论对本文应用作。。C0.1μm。关键词:光传输;散射理论;MieC@H2O复合粒子;散射特性收稿日期:基金项目:国家自然科学基金(2018-05-21;修订日期:2018-08-26，1134715861704149SupportedbyNationalNaturalScienceFoundationofChinaZaozhuangUniersity102061803());枣庄学院青年科学基金(，11347158102061803);61704149()资助项目ProjectofYouthScientificResearchFundof第3期LYUYi-ying，etal.:ScatteringCharacteristicsofC@H2OCompositeParticleBasedonMieLight…2991IntroductionNowadays，lasercommunicationtechnologyhasnecessarytostudytheintensitydistribution，polari-zationchangeandotherfactorsthatmayinfluencethetheelectromagneticwaveafterscatteringbymi-developedrapidlywiththeimprovementoflaserper-croparticles.formance.Ithasthefollowingadvantagesoflargein-formationcapacitygoodsecrecylightstructureand，，practicality.Hightransmissionefficiencyisone[]1-3，ofthekeyfactorsinthedevelopmentoflasertech-nology.Howeverthescatteringoflightintheat-mospherewillmakegreateffectonthepropagationoflaserintheupperair.Therearesomearticlesabouttheinfluenceofairborneparticlesonlasercommuni-[]4-6，cation.Asitisputparticleswereregardedassinglespheresinmostofthemwhileinfactmagnani-identifiedasacoreinthecenterwhileanotheror，mousofwhichhaveacompositeparticlestructure.severaldifferentsubstancesarecoatedontheoutsideOneoftheresearchhotspotsinopticalcommunica-toformshells.Fig.1Core-shellstructurediagram.Theso-calledcore-shellstructureisakindofstructurethatasubstanceistionistoachievehightransmissionefficiencybe-tweentargetswhilethelightscatteringofalargenumberofparticlesintheatmosphereaffectstheef-ficiencyoflasertransmission.，InthispaperthescatteringpropertiesofC@H2OcoreshellstructuredparticlesarestudiedbyusingtheMiescatteringtheory.TheMiescatteringtheoryiswidelyusedinparticlescatteringre-search[7-12].Inviewofthelargenumberofwatermoleculesintheairitishelpfultostudythescat-，teringcharacteristicsoftheC@H2Onuclearshellparticlesasfortomakethein-depthstudyofthela-serfieldtransmission.Wehopethatitcanprovidesometheoreticalguidanceforimprovingthetrans-missionefficiencyofopticalcommunication.2TheoreticalPrinciple2.1Core-shellStructureThestructureofcore-shellstructureisshowninFig.1.Therearealargenumberofcompositemicro-particlesintheatmosphere，smallcoherentnucleus，，withwidedistributionofparticlesizessurroundedwithwater.ThecontentofC@H2Ocompositeparti-clesisveryhighintheatmosphereastheproportionofwatervaporintheatmosphereiscloseto4%.Re-searchesontheopticalpropertiesof[havebeenreportedinsomepapers13-14theparticles]，anditishavingthestructureofaleltothepolarizedopticalvector.Thedegreeofpo-suchascarboninthecenterlarizationisgivenbyformula3():2.2MieScatteringTheoryForaregularsphericalscatter，whenthewave-，lengthoftheelectromagneticfieldthatincidenttothescatteriscomparabletothesizeofitthescat-teringcharactersofthescatteragainsttheelectro-magneticfieldcanbeprocessedaccuratelybytheMiescatteringtheory.TheshapeofC@H2Ointheatmospherecanberegardedasspherebecauseitsra-diusissmallincaseofnonabnormalweather[]15.Thescatteringintensitycanbecalculatedbythefollowingformulaaccordingtothe()1()2andMiescatteringtheory.Andthesetwoformulasareusedforpartialpolarizedlight:I⊥=I∥=，，λ28π2r2I0i1λ28π2r2I0i2(())12WhereI⊥isthescatteringintensityofopticalvectorthatperpendiculartothepolarizedopticalvectorI∥isthescatteringintensityofopticalvectorthatparal-;，Here)i1=s1(P=，，)aθ)(，θm，a·s*2am;functionsofscatteringlight;functionsofscatteredlight.Wherei1s1s*·s*1)(((，);，a3，θI⊥-I∥I⊥+I∥，mθ，i2aretheintensity，s2aretheamplitude，s*2aretheconjugatei2=s2m1，300发光学报第40卷，complexofs1parameteroftheparticles2respectively(s1;;θa=πD/λisthesize)()ands2θaretwoamplitudefunctionsrelatedtothescatteringanglewhoseexpressionsareasformula4():()θs1θ=∑n=12n+1(n+1)n()θs2#=∑n=1(()1nPcosθ2n+1(nn+1))(dPn=sinθ)cosθdsinθhereπn=((anπn+bnπn)anπn+bnπn)，()4()thefirst-ordern-timesfirst-classLegendrefunctioncosθisthefirstLegendrefunctionPncalledtheMiecoefficientandcanbecalculatedbyaandbare，P()1n()cosθis;;theformula{(((5):)a)a((mψnmζna=ψnζnbn=))((ψ'ψ'n))aamama((ψ'nψ'nmama(-mψ'n(-mζ'n)))a)a(-ψ'n(-ζ'n(ψn(ψn)a)a)ma)ma(ψn(ψn)ma)ma}，(()zz=zJnWhereψnsphericalBesselfunction)，ofthefirstkind(ψ'nz)(()，ζ，Hnandζ'na=zHn)z()a()z)5is(z)，Jn(isHankelfunctionarethederiva-tiveswithrespecttotheirvariables.3ResultsandDiscussion3.1ScatteringIntensityofC@H2OCompositePartizcleFig.2Thescatteringintensityagainstscatteringangle，，atdifferentincidentwavelengthsnuclearradius()andwaterfilmthicknesswereplottedinFig.2(.Forthepurposeofdiscussingthepropertiesofca)scatteringintensityonC@H2Ocompositeparticles.andTheforwardscatteringgivesdominance，thescatteringintensityfirstdecreasesandthenin-creasesslightlywiththeincreaseofthescatteringan-gleforacertainincidentwavelengthaccompanied，scatteringangleof100°asisshowninFig.2，()a.Therelationshipbetweenscatteringintensityandin-cidentangleatdifferentnuclearradiusisshowninFig.2bwiththeincidentwavelength0.532μm()，andthethicknessofwaterfilm1μm.Itcanbeseenthatwhenthecarboncoreradiusisfixedtheforward，ScatteringintensityofC@H2Ocompositeparticlesatdifferentincidentwavelengthsdifferentnuclear)，a(()，radiusbdifferentwaterfilmthickness.The()c-scatteringintensitydecreaseswiththeincreaseofin-，cidentwavelengthinacertainrange.Withfixedcar-boncoreradiustheforwardscatteringdominatesandthescatteringintensityfirstdecreasesthenincreasesatabout80°followedwithacertainoscillation.Inho-mogeneousoscillationsonthedistributionofscatteringintensityareobviouswhenthethicknessofwaterfilmis()larger1μmand2μm.Meanwhilethescattering，，tobestablearound60°whenthethicknessissmaller()0.05μmand0.1μm.firstdecreasesthenincreasesatabout80°followedwithacertainoscillation.Thecurvesaresimilarlyunderdifferentcarbonradiuswhereastheparticleswithbiggercarboncoreradiushavestrongerscatter-byasmalloscillationandfinallystabilizedneartheintensitydecreaseswiththeincreaseofangleandtendsscatteringdominatesandthescatteringintensityingintensityinlargeangelscattering.Todiscussthe第3期LYUYi-ying，etal.:ScatteringCharacteristicsofC@H2OCompositeParticleBasedonMieLight…301influenceofwaterfilmthicknessthecurveofscatter-，tinglinearlypolarizedlightappearedhere.Mean-，ingintensityagainstscatteringangleisplottedatin-whilethenumberofpolarizationpeaksincreasescidentwavelengthof0.532μmandcoreradiusof3.Theforwardscatter-μmasisshowninFig.2，c()obviouslyandtheforwardpolarizationadvantageisobviouswiththeincreaseofwaterfilmthickness.ingalsodominateswhenthethicknessofwaterfilmThusitcanbeconcludedthatwaterfilmthicknessisfixedaswithfixedcarboncoreradius.Asfordif-hasimportantinfluenceonthepolarizationofparticle.，ferentthicknessinhomogeneousoscillationsonthedistributionofscatteringintensityareobviouswhenthethicknessofwaterfilmislarger1μmand2(whilescatteringintensitydecreaseswiththe)，μmincreaseofangle，whenthethicknessissmallerandtendstobestablearound60°()0.05μmand0.1μm.Inadditionitcanalsobeseenthattheforwardscat-，teringvariedobviouslywiththeincreaseofthewaterfilmthicknesswhilethebackscatteringisopposite.3.2DegreeofPolarization，，Thepolarizationagainstscatteringangleatdif-ferentincidentwavelengthsnuclearradiusandwa-，terfilmthicknesswereplottedinFig.3.Thepolarizationfirstascendedthendescended，withtheincreasingofangleexhibitingobviousos-cillationwhichdiminishgraduallyastheanglein-creasesandthemostobviousphenomenonoccurswhenthewavelengthis0.325μmFig.3a().Therearemagnanimouspeaksforwhichasisshownin，thevalueofpolarizationcloseto1inlargerincidentwavelengths.Minimumpolarizationappearsat0.325μmwavelengthintheforwardscatteringanddepo-larizationoccursinothersitesbeyondthepeakfull，，depolarizationispresentinbothforwardandback-wardscattering.Therelationshipsbetweenpolariza-tionandscatteringangleunderdifferentcarbonradi-usareshowninFig.3bwiththeincidentwave-()，lengthis0.532μmandwaterfilmthicknessis1μm.AlthoughtheimagesinFig.3arenotsoclearlyitstillcanbeseenthatthepolarizationsfirst()bascendandthendescendwiththeincreasingofan-，，gleandthenumberofpeaksaddsasthecarbonra-obviousperformancewiththewavelengthof0.325μm.()cdiusincreases.Theprofilesofpolarizationatdiffer-Minimumpolarizationappearsat0.325μmwave-entwaterfilmthicknesswereshowninFig.3inlengthintheforwardscatteringanddepolarizationfavorofanalyzingthevariationofpolarizationcom-，()，prehensivelywiththeincidentwavelengthis0.532μmandthecarboncoreradiusis3μm.AsisshowninFig.3ctherearemultiplepeaksatdifferentthicknesseswhosepolarizationarecloseto1indica-，occursinothersitesbeyondthepeak.Therearepeakswhosepolarizationiscloseto1whichindicateslinearlypolarizedlightappeared.3.3OpticalCrossSectionThescatteringcrosssection，extinctioncrossFig.3PolarizationofC@H2Ocompositeparticlesatdiffer-differentnuclearradius)，a(entincidentwavelengths()，bdifferentwaterfilmthickness.Thepolari-()czationexhibitingobviousoscillationthatdiminishedgraduallyastheangleincreasedandithasthemost，，302发光学报第40卷sectionandabsorptioncrosssectionagainstparticleradiuswereplottedinFig.4-6forthesakeoffur-therdiscussonthescatteringcharactersofC@H2Ocompositeparticle.Thescatteringcrosssectionincreasesfirstand，thendecreasesslightlywiththeincreaseoftheradi-usandreachesitsmaximumatabout0.1μm.Cer-tainoscillationswhicharetheresultoftheinterac-tionbetweenelectricdipoleandmagneticdipoleap-peared.Thegreatertheradiusthemoreobviousthe，concussionandfinallygraduallystabilized.Thepo-，sitionofthefirstpeakmovestowardthedirectionofradiusasthewavelengthincreasedasisshowninFig.4.Theextinctioncrosssectionhasthesimilar，charactersasthescatteringcrosssectionasis-，Fig.6Relationshipbetweentheextinctioncrosssectionandtheparticleradiusunderdifferentwavelengths.Theabsorptioncrosssectionincreasesfirstandthende-creasesastheradiusincreasesandobviousoscilla-，tionsappeared.Themaximumpeakmovestowardtothedirectionofradiusasthewavelengthincreased.showninFig.5.ThecurvesoftheextinctioncrosssectionagainsttheparticleradiusareplottedinFig.，6.Theabsorptioncrosssectionincreasesfirstandthendecreasesastheradiusincreasesobviousos-cillationswhicharetheresultoftheinteractionbe-tweenelectricdipoleandmagneticdipoleappear.Themaximumpeakmovestowardthedirectionofra-diusasthewavelengthincreased.4ConclusionThescatteringcharacteristicsofC@H2Ocom-Fig.4Relationshipbetweenscatteringcrosssectionandra-positesphericalparticlesaregiveninthispaper.Itdiusunderdifferentincidentwavelengths.Thescatter-isfoundthattheincidentwavelengthradiusoftheingcrosssectionincreasesfirstandthendecreasescoreandthethicknessofthewaterfilmallhaveslightlywiththeincreaseoftheradiusandreachesgreatinfluenceontheforwardscatteringintensity.itsmaximumatabout0.1μm.Thegreatertheradi-Thelargertheincidentwavelengthusthemoreobvioustheconcussionandfinallyscatteringintensitythelargerthenuclearradius;theweakerthe，，，，，，，graduallystabilized.Fig.5Relationshipbetweenextinctioncrosssectionandra-diusunderdifferentincidentwavelengths.Theex-tinctioncrosssectionincreasesfirstandthendecrea-sesslightlywiththeincreaseoftheradiusandrea-chesitsmaximumatabout0.1μm.Ithasthesimi-larlycharacterstotheextinctioncrosssection.thethickerthewaterfilmthicknessthestrongertheforwardscattering.However，therearenoobvious，changesonthebackscattering.Asamatteroffacttheincidentwavelengthcarbonnuclearradiusand，waterfilmthicknessallhavetheinfluenceonpolari-zation.Thepeakvalueofthepolarizationiscloseto1thatmeanslinearlypolarizedlightappearedinsev-eralsiteswithlargerincidentwavelengths.Therearemorepolarizationpeaksonlargernuclearradius.Andthenumberofpeaksaddswiththeincreasedwaterfilmthickness.Theopticalcrosssectionisaf-fectedbytheincidentwavelengthasfollowingsthe:，maximumpeakoftheopticalcrosssectionmovesto-wardthedirectionofradiuswiththeincreasingofinci-dentwavelengthaccompaniedbycertainoscillations.，][1，(，2):2005Rep.345-396.]曾飞，高世杰，伞晓刚，等.4第3期LYUYi-ying，etal.:ScatteringCharacteristicsofC@H2OCompositeParticleBasedonMieLight…303References:MAJUMDARAK.Free-spacelasercommunicationperformanceintheatmosphericchannel[]J.J.Opt.FiberCommun.[2[3[4(1Opt.，92016ZENGF，，GAOSJ):机载激光通信系统发展现状与趋势[].中国光学，2016J，etal..Developmentstatusandtrendofairbornelasercommunicationterminals，SANXG(]天空背景光对空间激光通信系统的影响[.激光与光电子学进展，2017J65-73.]范新坤，张磊，佟首峰，等.，TONGSF，)，54]非视线光散射通信的大气传输模型[.中国激光，2006JserOptoelectron.Prog.]冯涛，陈刚，方祖捷.，FANGZJ.Atmosphericpropagationmodelinnon-line-of-sightopticalscatteringcommunication，etal..Influenceofskybackgroundlightonspacelasercommunicationsystem(，ZHANGL1522-1526.inChineseinChineseFANXKFENGT070601.，(5465-73.，33):72017，9070601.[]J):):):1117()((.La-][J.[]J.Chin.，CHENG，Chin.J.Lasers，YANGJKCHANGSL200611):(，33，YANGJC1522-1526.inChinese()，WirelessCommunicationsandNetworks，Wuhan，5284:20041621-31.，etal..TheexperimentalresearchofUVcommunication[]C.ProceedingsofSPIE[5][6][7][8[9]]614-631.1700256.():，2013，38anicEng.，，KIMJHSHIMTS(，CHOS4，292017，ZHOUN):22，SHILMater.YUANW[]JMISHCHENKOMIVANWALREEPA.Propagationandscatteringeffectsinunderwateracousticcommunicationchannels[]J.IEEEJ.Oce-，etal..SelectivecolorationofmelaninnanospheresthroughresonantMiescattering[]J.Adv.，etal..StructuralcolorationofcolloidalfiberbyphotonicbandgapandresonantMiescattering.ACSAppl.Mater.Interfaces20152514064-14071.，(，7):FORTRANprogram[]徐庆君，庄申栋.10，YANGP.Far-fieldLorenz-Miescatteringinanabsorbinghostmedium[]J基于241-252.]散射理论对砷化镓光子晶体安德森定域化研究[.强激光与粒子束，2011J.J.Quant.Spectrosc.Radiat.Transfer，2052018Mie，::theoreticalformalismand，232613-2616.，ZHUANGSD.StudyonAndersonlocalizationofphotoniccrystalofGaAsbasedonMiescatteringtheoryXUQJ，HighPowerLaserPart.Beams基于]徐庆君，韦德泉，田贵才.2011Mie(10):，23]散射理论的铌酸锂晶粒散射特性[.发光学报，2009J2613-2616.inChinese()[11(，306):867-871.Chin.J.Lumin.]徐庆君，田贵才.[12XUQJXUQJ，，TIANGC.ThescatteringcharacteristicsofLiNbO3particlebasedonMielightscatteringtheoryWEIDQ，2009基于(6，]散射理论的反蛋白石光子晶体定域化研究[.量子电子学报，2009J26[]J，TIANGC.LocalizationofreverseopalphotoniccrystalbasedonMielightscatteringtheoryinChinese867-871.，30Mie):):6()(698-702..Chin.J.Quan-[13，，26tumElectron.(6]吴良海，高隽，范之国，等.，FANZGWULH2009inChinese):698-702.大气粒子散射特性及其对空间偏振分布的影响[].光学学报，2011J，etal..Scatteringofparticlesintheatmosphereandtheirinfluenceoncelestialpolarization0701005.，31):7()(，GAOJ[]J，HULSTHC.Reviewofpublications-lightscatteringbysmallparticles.ActaOpt.SinicainChinese0701005.，312011，):7(()[]J.J.R.Astron.Soc.Can.，1960，():10][J.][J.[]14patternsVANDE():54589.[]王蓉蓉，吴振森，张艳艳，等.15WANGRRPart.Beams，WUZS，，262014，ZHANGYY():11153-159.(inChinese)]太赫兹波在雾中的多重散射特性[.强激光与粒子束，2014J，etal..MultiplescatteringcharacteristicsofTHzwaveinfog，(26[]J):153-159.11.HighPowerLaser1981-)，女，山东济宁人，硕吕依颖(士，讲师，年于天津大学获得硕士学位，主要从事光学理论和实验的研究2007。:E-maillyy100325@163.com1979-)，男，山东滕州人，博徐庆君(士，副教授，年于南开大学获得博士学位，主要从事固体光散射与光电功能材料方面的研究2006。:E-mailwlxqj@126.com
